Limit State Method MCQ with answer and solution

Concept

In the IS 456 stress block, the parabolic part ends at strain 0.002 and the rectangular part runs from 0.002 to 0.0035.

Step-by-step solution

1. Strain at top fibre = 0.0035. Strain at the NA = 0. 2. Strain varies in a straight line with depth. 3. Strain 0.002 occurs at (0.002/0.0035) xᵤ = (4/7) xᵤ from the NA. 4. So the parabolic part has depth (4/7) xᵤ. 5. The rectangular part has depth xᵤ − (4/7) x_u = (3/7) xᵤ. 6. Ratio of parabolic to rectangular depth = (4/7)/(3/7) = 4/3.

Explanation

he stress block has two parts. The parabolic part covers strain 0 to 0.002. The rectangular part covers strain 0.002 to 0.0035. Because strain is linear with depth, the parabolic depth is 4/7 xᵤ and the rectangular depth is 3/7 xᵤ. Their ratio is 4/3.

Why the other options are wrong

A (3/7) is the rectangular depth as a fraction of xᵤ, not the ratio. B (4/7) is the parabolic depth as a fraction of xᵤ, not the ratio. C (3/4) is the inverse ratio (rectangular to parabolic).